eprintid: 10055490 rev_number: 20 eprint_status: archive userid: 608 dir: disk0/10/05/54/90 datestamp: 2018-09-06 09:43:32 lastmod: 2021-09-25 23:08:46 status_changed: 2018-09-06 09:43:32 type: article metadata_visibility: show creators_name: Conrad, J creators_name: Chamberland, C creators_name: Breuckmann, NP creators_name: Terhal, BM title: The small stellated dodecahedron code and friends ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 keywords: Science & Technology, Multidisciplinary Sciences, Science & Technology - Other Topics, quantum error correction, fault tolerance, homological quantum codes, ERROR-CORRECTION, QUANTUM note: Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited. abstract: We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for three-dimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity check measurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop fault-tolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuit-based pseudo-threshold. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’. date: 2018-07-13 date_type: published publisher: ROYAL SOC official_url: https://doi.org/10.1098/rsta.2017.0323 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green article_type_text: Article verified: verified_manual elements_id: 1579615 doi: 10.1098/rsta.2017.0323 lyricists_name: Breuckmann, Nikolas lyricists_id: NPBRE98 actors_name: Bracey, Alan actors_id: ABBRA90 actors_role: owner full_text_status: public publication: Philosophical Transactions of The Royal Society A - Mathematical, Physical and Engineering Sciences volume: 376 number: 2123 article_number: 20170323 pages: 19 issn: 1471-2962 citation: Conrad, J; Chamberland, C; Breuckmann, NP; Terhal, BM; (2018) The small stellated dodecahedron code and friends. Philosophical Transactions of The Royal Society A - Mathematical, Physical and Engineering Sciences , 376 (2123) , Article 20170323. 10.1098/rsta.2017.0323 <https://doi.org/10.1098/rsta.2017.0323>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10055490/1/20170323.full.pdf